Irreversible Investment under Volatility Ambiguity 

Abstract

We present the first formal verification theorem for optimal stopping problems under G-Brownian motion in the economics literature. Our theorem provides sufficient conditions to verify the value function of such problems, applicable to real option analysis involving both drift and volatility ambiguity in the infinite horizon. We apply our theorem to study the irreversible investment problem and show that volatility ambiguity prompts early investment, as the worst-case scenario reflects the lowest possible volatility for the call-like investment option. In contrast, both volatility itself and drift ambiguity delay investment. These results suggest that volatility ambiguity can explain why firms like OpenAI rapidly advance the development of artificial intelligence models despite high uncertainty.

Keywords: Irreversible investment, real option, optimal stopping, volatility ambiguity, G-Brownian motion JEL code-C61